1. ## Permutations

I don't know how to do this question. Can someone help me?
There are 3 boys and 9 girls. But there are only 5 seats. The 3 boys must sit in the middle. The leftover seats are for the girls. How many ways can this be arranged?

2. ## Re: Permutations

Originally Posted by GuMing
I don't know how to do this question. Can someone help me?
There are 3 boys and 9 girls. But there are only 5 seats. The 3 boys must sit in the middle. The leftover seats are for the girls. How many ways can this be arranged?
How many ways can you arrange the boys in the middle?
How many ways can you seat a girl next to the first boy in the row?
Then, how many ways can you seat a girl next to the last boy in the row?

3. ## Re: Permutations

So there are 6 ways in which i can arrange the boys in the middle
And there are 6 x 6P1 = 36 ways in which a girl sit next to the first boy
Then, there are 36 x 5P1 = 180 ways in which another can sit next to the last boy

Is that right?

4. ## Re: Permutations

Originally Posted by GuMing
So there are 6 ways in which i can arrange the boys in the middle
And there are 6 x 6P1 = 36 ways in which a girl sit next to the first boy
Then, there are 36 x 5P1 = 180 ways in which another can sit next to the last boy
BUT there are nine girls not six.